On an Aitken type method

Authors

  • Ion Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
  • Emil Cătinaş Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords:

nonlinear equations, Aitken method

Abstract

In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear equations in \({\mathbb R}\). We obtain conditions which assure monotone convergence of the generated sequences. We also obtain a posteriori estimations for the errors.

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References

M.A. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York and London, 1980.

I. Păvăloiu, Solutions Equations by Interpolation, Dacia, Cluj-Napoca, 1981 (in Romanian).

I. Păvăloiu, Bilateral approximation of solution of equations by order three Steffensen-type methods, Studia Univ. "Babeş-Bolyai", Mathematica, LI (2006) no. 3, pp. 105-114.

I. Păvăloiu, and N. Pop, Interpolation and Applications, Risoprint, Cluj-Napoca, 2005 (in Romanian).

I. Păvăloiu, Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32 (1995) nos. 1-2, pp. 69-82, https://doi.org/10.1007/bf02576543

I. Păvăloiu and E. Cătinaş, On a Steffensen type method, Proceedings of the Ninth International Symposion on Symbolic and Numeric Algoritms for Scientific Computing (SYNASC 2007), September 26-29, 2007, Timişoara, Romania, IEEE Computer Society, pp. 369-375.

B.A. Turowicz, Sur les derivées d'ordre superieur d'une fonction inverse, Ann. Polon. Math., 8 (1960), pp. 265-269, https://doi.org/10.4064/ap-8-3-265-269 .

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Published

2007-08-01

How to Cite

Păvăloiu, I., & Cătinaş, E. (2007). On an Aitken type method. Rev. Anal. Numér. Théor. Approx., 36(2), 173–176. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art5

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